accepted, it was presented in an entirely new point of view
by being combined with the facts of _polarization_. The
general idea of polarization must be illustrated hereafter;
but we may here remark that Young and Fresnel, who had
adopted the undulatory theory, after being embarrassed for
some time by the new facts which were thus presented to
their notice, at last saw that these facts might be
explained by conceiving the vibrations to be transverse to
the ray, the motions of the particles being not backwards
and forwards in the line in which the impulse travels, but
to the right and left of that line. This conception of
_transverse vibrations_, though quite unforeseen, had
nothing in it which was at all difficult to reconcile with
the general notion of an undulation. We have described an
undulation, or wave, as a certain condition or arrangement
of the particles of the fluid successively transferred from
one part of space to another: and it is easily conceivable
that this arrangement or wave may be produced by a lateral
transfer of the particles from their quiescent positions.
This conception of transverse vibrations being accepted, it
was found that the explanation of the phenomena of
polarization and of those of interference led to the same
theory {330} with a correspondence truly wonderful; and this
coincidence in the views, collected from two quite distinct
classes of phenomena, was justly considered as an almost
demonstrative evidence of the truth of this undulatory
theory.
It remained to be considered whether the doctrine of
transverse vibrations in a fluid could be reconciled with
the principles of Mechanics. And it was found that by making
certain suppositions, in which no inherent improbability
existed, the hypothesis of transverse vibrations would
explain the laws, both of interference and of polarization
of light, in air and in crystals of all kinds, with a
surprizing fertility and fidelity.
Thus the Undulatory Theory of Light, like the Undulatory
Theory of Sound, is recommended by its conformity to the
fundamental principle of the Secondary Mechanical Sciences,
that the medium must be supposed to transmit its peculiar
impulses according to the laws of Mechanics. Although no one
had previously dreamt of qualities being conveyed through a
medium by such a process, yet when it is once suggested as
the only mode of explaining some of the phenomena, there is
nothing to prevent our accepting it entirely, as a
satisfactory theory for all the known laws of Light.
4. _Heat._--With regard to Heat as with regard to Light, a
fluid medium was necessarily assumed as the vehicle of the
property. During the last century, this medium was supposed
to be an emitted fluid. And many of the ascertained Laws of
Heat, those which prevail with regard to its radiation more
especially, were well explained by this hypothesis[22\4].
Other effects of heat, however, as for instance _latent
heat_[23\4], and the change of _consistence_ of
bodies[24\4], were not satisfactorily brought into connexion
with the hypothesis; while {331} _conduction_[25\4], which
at first did not appear to result from the fundamental
assumption, was to a certain extent explained as internal
radiation.
[Note 22\4: See the Account of the Theory of Exchanges,
_Hist. Ind. Sc._ b. x. c. i. sect. 2.]
[Note 23\4: _Ib._ c. ii. sect. 3.]
[Note 24\4: _Ib._ c. ii. sect. 2.]
[Note 25\4: _Ib._ c. i. sect. 7.]
But it was by no means clear that an Undulatory Theory of
Heat might not be made to explain these phenomena equally
well. Several philosophers inclined to such a theory; and
finally, Ampère showed that the doctrine that the heat of a
body consists in the undulations of its particles propagated
by means of the undulations of a medium, might be so
adjusted as to explain all which the theory of emission
could explain, and moreover to account for facts and laws
which were out of the reach of that theory. About the same
time it was discovered by Prof. Forbes and M. Nobili that
radiant heat is, under certain circumstances, polarized. Now
polarization had been most satisfactorily explained by means
of transverse undulations in the case of light; while all
attempts to modify the emission theory so as to include
polarization in it, had been found ineffectual. Hence this
discovery was justly considered as lending great countenance
to the opinion that Heat consists in the vibrations of its
proper medium.
But what is this medium? Is it the same by which the
impressions of Light are conveyed? This is a difficult
question; or rather it is one which we cannot at present
hope to answer with certainty. No doubt the connexion
between Light and Heat is so intimate and constant, that we
can hardly refrain from considering them as affections of
the same medium. But instead of attempting to erect our
systems on such loose and general views of connexion, it is
rather the business of the philosophers of the present day
to determine the laws of the operation of heat, and its real
relation to light, in order that we may afterwards be able
to connect the theories of the two qualities. Perhaps in a
more advanced state of our knowledge we may be able to state
it as an Axiom, that two Secondary Qualities, which are
intimately connected in their causes and effects, must be
affections of the same Medium. {332} But at present it does
not appear safe to proceed upon such a principle, although
many writers, in their speculations both concerning Light
and Heat, and concerning other properties, have not
hesitated to do so.
Some other consequences follow from the Idea of a Medium
which must be the subject of another chapter.
{{333}}
CHAPTER IV.
OF THE MEASURE OF SECONDARY QUALITIES.
SECT. I.--_Scales of Qualities in general._
THE ultimate object of our investigation in each of the
Secondary Mechanical Sciences, is the nature of the
processes by which the special impressions of sound, light,
and heat, are conveyed, and the modifications of which these
processes are susceptible. And of this investigation, as we
have seen, the necessary basis is the principle, that these
impressions are transmitted by means of a medium. But before
we arrive at this ultimate object, we may find it necessary
to occupy ourselves with several intermediate objects:
before we discover the _cause_, it may be necessary to
determine the _laws_ of the phenomena. Even if we cannot
immediately ascertain the mechanism of light or heat, it may
still be interesting and important to arrange and measure
the effects which we observe.
The idea of a Medium affects our proceeding in this research
also. We cannot measure Secondary qualities in the same
manner in which we measure Primary qualities, by a mere
addition of parts. There is this leading and remarkable
difference, that while both classes of qualities are
susceptible of changes of magnitude, primary qualities
increase by addition of _extension_, secondary, by
augmentation of _intensity_. A space is doubled when another
equal space is placed by its side; one weight joined to
another makes up the sum of the two. But when one degree of
warmth is combined with another, or one shade of red colour
with another, we cannot in like manner talk of the _sum_.
The component parts do not evidently retain their {334}
separate existence; we cannot separate a strong green colour
into two weaker ones, as we can separate a large force into
two smaller. The increase is absorbed into the previous
amount, and is no longer in evidence as a part of the whole.
And this is the difference which has given birth to the two
words _extended_, and _intense_. That is extended which has
'partes extra partes,' parts outside of parts: that is
intense which becomes stronger by some indirect and
unapparent increase of agency, like the stretching of the
internal springs of a machine, as the term _intense_
implies. Extended magnitudes can at will be resolved into
the parts of which they were originally composed, or any
other which the nature of their extension admits; their
proportion is apparent; they are directly and at once
subject to the relations of number. Intensive magnitudes
cannot be resolved into smaller magnitudes; we can see that
they differ, but we cannot tell in what proportion; we have
no direct measure of their quantity. How many times hotter
than blood is boiling water? The answer cannot be given by
the aid of our feelings of heat alone.
The difference, as we have said, is connected with the
fundamental principle that we do not perceive Secondary
qualities directly, but through a Medium. We have no natural
apprehension of light, or sound, or heat, as they exist in
the bodies from which they proceed, but only as they affect
our organs. We can only measure them, therefore, by some
_Scale_ supplied by their effects. And thus while extended
magnitudes, as space, time, are measurable directly and of
themselves; intensive magnitudes, as brightness, loudness,
heat, are measurable only by artificial means and
conventional scales. Space, time, measure themselves: the
repetition of a smaller space, or time, while it composes a
larger one, measures it. But for light and heat we must have
Photometers and Thermometers, which measure something which
is assumed to be an indication of the quality in question.
In the one case, the mode of applying the measure, and the
meaning of the number resulting, are seen by intuition; in
the {335} other, they are consequences of assumption and
reasoning. In the one case, they are _Units_, of which the
extension is made up; in the other, they are _Degrees_ by
which the intensity ascends.
2. When we discover any property in a sensible quality,
which at once refers us to number or space, we readily take
this property as a measure; and thus we make a transition
from quality to quantity. Thus Ptolemy in the third chapter
of the First Book of his _Harmonics_ begins thus: 'As to the
differences which exist in sounds both in _quality_ and in
_quantity_, if we consider that difference which refers to
the acuteness and graveness, we cannot at once tell to which
of the above two classes it belongs, till we have considered
the causes of such symptoms.' But at the end of the chapter,
having satisfied himself that grave sounds result from the
magnitude of the string or pipe, other things being equal,
he infers, 'Thus the difference of acute and grave appears
to be a difference of _quantity_.'
In the same manner, in order to form Secondary Mechanical
Sciences respecting any of the other properties of bodies,
we must reduce these properties to a dependence upon
quantity, and thus make them subject to measurement. We
cannot obtain any sciential truths respecting the comparison
of sensible qualities, till we have discovered measures and
scales of the qualities which we have to consider; and
accordingly, some of the most important steps in such
sciences have been the establishment of such measures and
scales, and the invention of the requisite instruments.
The formation of the mathematical sciences which rest upon
the measures of the intensity of sensible qualities took
place mainly in the course of the last century. Perhaps we
may consider Lambert, a mathematician who resided in
Switzerland, and published about 1750, as the person who
first clearly felt the importance of establishing such
sciences. His Photometry, Pyrometry, and Hygrometry, are
examples of the systematic reduction of sensible qualities
(light, heat, moisture) to modes of numerical measurement.
{336}
We now proceed to speak of such modes of measurement with
regard to the most obvious properties of bodies.
SECT. II.--_The Musical Scale._
3. THE establishment of the _Harmonic Canon_, that is, of a
Scale and Measure of the musical place of notes, in the
relation of _high_ and _low_, was the first step in the
science of Harmonics. The perception of the differences and
relations of musical sounds is the office of the sense of
hearing; but these relations are fixed, and rendered
accurately recognizable by artificial means. 'Indeed, in all
the senses,' as Ptolemy truly says in the opening of his
Harmonics, 'the sense discovers what is approximately true,
and receives accuracy from another quarter: the reason
receives the approximately-true from another quarter, and
discovers the accurate truth.' We can have no measures of
sensible qualities which do not ultimately refer to the
sense;--whether they do this immediately, as when we refer
Colours to an assumed Standard; or mediately, as when we
measure Heat by Expansion, having previously found by an
appeal to sense that the expansion increases with the heat.
Such relations of sensible qualities cannot be described in
words, and can only be apprehended by their appropriate
faculty. The faculty by which the relations of sounds are
apprehended is a _musical ear_ in the largest acceptation of
the term. In this signification the faculty is nearly
universal among men; for all persons have musical ears
sufficiently delicate to understand and to imitate the
modulations corresponding to various emotions in speaking;
which modulations depend upon the succession of acuter and
graver tones. These are the relations now spoken of, and
these are plainly perceived by persons who have very
imperfect musical ears, according to the common use of the
phrase. But the relations of tones which occur in speaking
are somewhat indefinite; and in forming that musical scale
which is the basis of our science upon the subject, we {337}
take the most definite and marked of such relations of
notes; such as occur, not in speaking but in singing. Those
musical relations of two sounds which we call the _octave_,
the _fifth_, the _fourth_, the _third_, are recognized after
a short familiarity with them. These _chords_ or _intervals_
are perceived to have each a peculiar character, which
separates them from the relations of two sounds taken at
random, and makes it easy to know them when sung or played
on an instrument; and for most persons, not difficult to
sing the sounds in succession exactly, or nearly correct.
These musical relations, or _concords_, then, are the
groundwork of our musical series of sounds. But how are we
to name these indescribable sensible characters? how to
refer, with unerring accuracy, to a type which exists only
in our own perceptions? We must have for this purpose a
_Scale_ and a _Standard_.
The Musical Scale is a series of eight notes, ascending by
certain steps from the first or key-note to the octave above
it, each of the notes being fixed by such distinguishable
musical relations as we have spoken of above. We may call
these notes C, D, E, F, G, A, B, _c_; and we may then say
that G is determined by its being a fifth above C; D by its
being a fourth below G; E by its being a third above C; and
similarly of the rest. It will be recollected that the terms
a _fifth_, a _fourth_, a _third_, have hitherto been
introduced as expressing certain simple and indescribable
musical relations among sounds, which might have been
indicated by any other names. Thus we might call the fifth
the _dominant_, and the fourth the _subdominant_, as is done
in one part of musical science. But the names we have used,
which are the common ones, are in fact derived from the
number of notes which these intervals include in the scale
obtained in the above manner. The notes, C, D, E, F, G,
being five, the interval from C to G is a fifth, and so of
the rest. The fixation of this scale gave the means of
describing exactly any note which occurs in the scale, and
the method is easily applicable to notes above and below
this range; for in a series of sounds higher or lower by an
octave than {338} this standard series, the ear discovers a
recurrence of the same relations so exact, that a person may
sometimes imagine he is producing the same notes as another
when he is singing the same air an octave higher. Hence the
next eight notes may be conveniently denoted by a repetition
of the same letters, as the first; thus, C, D, E, F, G, A,
B, _c_, _d_, _e_, _f_, _g_, _a_, _b_; and it is easy to
devise a continuation of such cycles. And other admissible
notes are designated by a further modification of the
standard ones, as by making each note _flat_ or _sharp_;
which modification it is not necessary here to consider,
since our object is only to show how a standard is
attainable, and how it serves the ends of science.
We may observe, however, that the above is not an exact
account of the first, or early Greek scale; for that scale
was founded on a primary division of the interval of two
octaves (the extreme range which it admitted) into five
_tetrachords_, each tetrachord including the interval of a
fourth. All the notes of this series had different names
borrowed from this division[26\4]; thus _mese_ was the
middle or key-note; the note below it was _lichanos mesôn_,
the next below was _parypate mesôn_, the next lower, _hypate
mesôn_. The fifth above _mese_ was _nete diazeugmenôn_, the
octave was _nete hyperbolæôn_.
[Note 26\4: Burney's _History of Music_, vol. i. p. 28.]
4. But supposing a complete system of such denominations
established, how could it be with certainty and rigour
applied? The human ear is fallible, the organs of voice
imperfectly obedient; if this were not so, there would be no
such thing as a _good_ ear or a _good_ voice. What means can
be devised of finding at will a _perfect_ concord, a fifth
or a fourth? Or supposing such concords fixed by an
acknowledged authority, how can they be referred to, and the
authority adduced? How can we enact a Standard of sounds?
A Standard was discovered in the _Monochord_. A musical
string properly stretched, may be made to produce different
notes, in proportion as we intercept a longer or shorter
portion, and make this portion {339} vibrate. The relation
of the length of the strings which thus sound the two notes
G and C is fixed and constant, and the same is true of all
other notes. Hence the musical interval of any notes of
which we know the places in the musical scale, may be
reproduced by measuring the lengths of string which are
known to give them. If C be of the length 180, D is 160, E
is 144, F is 135, G is 120; and thus the musical relations
are reduced to numerical relations, and the monochord is a
complete and perfect _Tonometer_.
We have here taken the length of the string as the measure
of the tone: but we may observe that there is in us a
necessary tendency to assume that the ground of this measure
is to be sought in some ulterior cause; and when we consider
the matter further, we find this cause in the frequency of
these vibrations of the string. The truth that the same note
must result from the same frequency of vibration is readily
assented to on a slight suggestion of experience. Thus
Mersenne[27\4], when he undertakes to determine the
frequency of vibrations of a given sound, says 'Supponendum
est quoscunque nervos et quaslibet chordas unisonum
facientes eundem efficere numerum recursuum eodem vel equali
tempore, quod perpetuâ constat experientiâ.' And he proceeds
to apply it to cases where experience could not verify this
assertion, or at least had not verified it, as to that of pipes.
[Note 27\4: _Harmonia_, lib. ii. prop. 19.]
The pursuit of these numerical relations of tones forms the
science of Harmonics; of which here we do not pretend to
give an account, but only to show, how the invention of a
Scale and Nomenclature, a Standard and Measure of the tone
of sounds, is its necessary basis. We will therefore now
proceed to speak of another subject; _colour_.
SECT. III.--_Scales of Colour._
5. _The Prismatic Scale of Colour._--A SCALE of Colour must
depend originally upon differences {340} discernible by the
eye, as a scale of notes depends on differences perceived by
the ear. In one respect the difficulty is greater in the
case of the visible qualities, for there are no relations of
colour which the eye peculiarly singles out and
distinguishes, as the ear selects and distinguishes an
octave or a fifth. Hence we are compelled to take an
arbitrary scale; and we have to find one which is fixed, and
which includes a proper collection of colours. The
_prismatic spectrum_, or coloured image produced when a
small beam of light passes obliquely through any transparent
surface (as the surface of a prism of glass,) offers an
obvious Standard as far as it is applicable. Accordingly
colours have, for various purposes, been designated by their
place in the spectrum, ever since the time of Newton; and we
have thus a means of referring to such colours as are
included in the series _red_, _orange_, _yellow_, _green_,
_blue_, _violet_, _indigo_, and the intermediate tints.
But this scale is not capable of numerical precision. If the
spectrum could be exactly defined as to its extremities, and
if these colours occupied always the same proportional part
of it, we might describe any colour in the above series by
the measure of its position. But the fact is otherwise. The
spectrum is too indefinite in its boundaries to afford any
distinct point from which we may commence our measures; and
moreover the spectra produced by different transparent
bodies differ from each other. Newton had supposed that the
spectrum and its parts were the same, so long as the
refraction was the same; but his successors discovered that,
with the same amount of refraction in different kinds of
glass, there are different magnitudes of the spectrum; and
what is still worse with reference to our present purpose,
that the spectra from different glasses have the colours
distributed in different proportions. In order, therefore,
to make the spectrum the scale of colour, we must assume
some fixed substance; for instance, we may take water, and
thus a series approaching to the colours of the _rainbow_
will be our standard. But we should still have an extreme
difficulty in applying such a rule. The distinctions of
{341} colour which the terms of common language express, are
not used with perfect unanimity or with rigorous precision.
What one person calls _bluish green_ another calls _greenish
blue_. Nobody can say what is the precise boundary between
red and orange. Thus the prismatic scale of colour was
incapable of mathematical exactness, and this inconvenience
was felt up to our own times.
But this difficulty was removed by a curious discovery of
Wollaston and Fraunhofer; who found that there are, in the
solar spectrum, certain fine black Lines which occupy a
definite place in the series of colours, and can be observed
with perfect precision. We have now no uncertainty as to
what coloured light we are speaking of, when we describe it
as that part of the spectrum in which Fraunhofer's Line C or
D occurs. And thus, by this discovery, the prismatic
spectrum of sunlight became, for certain purposes, an exact
_Chromatometer_.
6. _Newton's Scale of Colours._--Still, such a standard,
though definite, is arbitrary and seemingly anomalous. The
lines A, B, C, D, &c., of Fraunhofer's spectrum are
distributed without any apparent order or law; and we do
not, in this way, obtain numerical measures, which is what,
in all cases, we desire to have. Another discovery of
Newton, however, gives us a spectrum containing the same
colours as the prismatic spectrum, but produced in another
way, so that the colours have a numerical relation. I speak
of the laws of the _Colours of Thin Plates_. The little
rainbows which we sometimes see in the cracks of broken
glass are governed by fixed and simple laws. The kind of
colour produced at any point depends on the thickness of the
thin plate of air included in the fissure. If the thickness
be eight-millionths of an inch, the colour is orange, if
fifteen-millionths of an inch, we have green, and so on; and
thus these numbers, which succeed each other in a regular
order from red to indigo, give a numerical measure of each
colour; which measure, when we pursue the subject, we find
is one of the bases of all optical theory. The series of
colours obtained from plates of air of gradually increasing
thickness is called {342} _Newton's Scale of Colours_; but
we may observe that this is not precisely what we are here
speaking of, a scale of _simple_ colours; it is a series
produced by certain combinations, resulting from the
repetition of the first spectrum, and is mainly useful as a
standard for similar phenomena, and not for colour in
general. The real scale of colour is to be found, as we have
said, in the numbers which express the thickness of the
producing film;--in the length of a _fit_ in Newton's
phraseology, or the length of an _undulation_ in the modern
theory.
7. _Scales of Impure Colours._--The standards just spoken of
include (mainly at least) only pure and simple colours; and
however complete these standards may be for certain objects
of the science of optics, they are insufficient for other
purposes. They do not enable us to put in their place mixed
and impure colours. And there is, in the case of colour, a
difficulty already noticed, which does not occur in the case
of sound; two notes, when sounded together, are not
necessarily heard as one; they are recognized as still two,
and as forming a concord or a discord. But two colours form
a single colour; and the eye cannot, in any way, distinguish
between a green compound of blue and yellow, and the simple,
undecomposable green of the spectrum. By composition of
three or more colours, innumerable new colours may be
generated which form no part of the prismatic series; and by
such compositions is woven the infinitely varied web of
colour which forms the clothing of nature. How are we to
classify and arrange all the possible colours of objects, so
that each shall have a place and name? How shall we find a
_chromatometer_ for impure as well as for pure colour?
Though no optical investigations have depended on a scale of
impure colours, such a scale has been wanted and invented
for other purposes; for instance, in order to identify and
describe objects of natural history. Not to speak of earlier
essays, we may notice Werner's Nomenclature of Colours,
devised for the purpose of describing minerals. This scale
of colour was far superior to any which had previously been
promulgated. {343} It was, indeed, arbitrary in the
selection of its degrees, and in a great measure in their
arrangement; and the colours were described by the usual
terms, though generally with some added distinction; as
_blackish green_, _bluish green_, _apple-green_,
_emerald-green_. But the great merit of the scale was its
giving a _fixed_ conventional meaning to these terms, so
that they lost much of their usual vagueness. Thus
_apple-green_ did not mean the colour of any green apple
casually taken; but a certain definite colour which the
student was to bear in mind, whether or not he had ever seen
an apple of that exact hue. The words were not a
description, but a _record_ of the colour: the memory was to
retain a _sensation_, not a name.
The imperfection of the system (arising from its arbitrary
form) was its incompleteness: however well it served for the
reference of the colours which it did contain, it was
applicable to no others; and thus though Werner's
enumeration extended to more than a hundred colours, there
occur in nature a still greater number which cannot be
exactly described by means of it.
In such cases the unclassed colour is, by the Wernerians,
defined by stating it as intermediate between two others:
thus we have an object described as _between emerald-green
and grass-green_. The eye is capable of perceiving a
gradation from one colour to another; such as may be
produced by a gradual mixture in various ways. And if we
image to ourselves such a mixture, we can compare with it a
given colour. But in employing this method we have nothing
to tell us in what part of the scale we must seek for an
approximation to our unclassed colour. We have no rule for
discovering where we are to look for the boundaries of the
definition of a colour which the Wernerian series does not
supply. For it is not always between contiguous members of
the series that the undescribed colour is found. If we place
emerald-green between apple-green and grass-green, we may
yet have a colour intermediate between emerald-green and
leek-green; and, in fact, the Wernerian series of colours is
destitute {344} of a principle of self-arrangement and
gradation; and is thus necessarily and incurably imperfect.
8. We should have a complete Scale of Colours, if we could
form a series including all colours, and arranged so that
each colour was intermediate in its tint between the
adjacent terms of the series; for then, whether we took many
or few of the steps of the series for our standard terms,
the rest could be supplied by the law of continuity; and any
given colour would either correspond to one of the steps of
our scale or fall between two intermediate ones. The
invention of a Chromatometer for Impure Colours, therefore,
requires that we should be able to form all possible colours
by such intermediation in a systematic manner; that is, by
the mixture or combination of certain elementary colours
according to a simple rule: and we are led to ask whether
such a process has been shown to be possible.
The colours of the prismatic spectrum obviously do form a
continuous series; green is intermediate between its
neighbours yellow and blue, orange between red and yellow;
and if we suppose the two ends of the spectrum bent round to
meet each other, so that the arrangement of the colours may
be circular, the violet and indigo will find their
appropriate place between the blue and red. And all the
interjacent tints of the spectrum, as well as the ones just
named, will result from such an arrangement. Thus all the
_pure_ colours are produced by combinations two and two of
three primary colours, Red, Yellow, and Blue: and the
question suggests itself whether these three are not really
the only Primary Colours, and whether all the impure colours
do not arise from mixtures of the three in various
proportions. There are various modes in which this
suggestion may be applied to the construction of a scale of
colours; but the simplest, and the one which appears really
to verify the conjecture that all possible colours may be so
exhibited, is the following. A certain combination of red,
yellow, and blue, will produce black, or pure grey, and when
diluted, will give all the shades of grey which intervene
between {345} black and white. By adding various shades of
grey, then, to pure colours, we may obtain all the possible
ternary combinations of red, yellow, and blue; and in this
way it is found that we exhaust the range of colours. Thus
the circle of pure colours of which we have spoken may be
accompanied by several other circles, in which these colours
are tinged with a less or greater shade of grey; and in this
manner it is found that we have a perfect chromatometer;
every possible colour being exhibited either exactly or by
means of approximate and contiguous limits. The arrangement
of colours has been brought into this final and complete
form by M. Merimée, whose Chromatic Scale is published by M.
Mirbel in his _Elements of Botany_. We may observe that such
a standard affords us a numerical exponent for every colour
by means of the proportions of the three primary colours
which compose it; or, expressing the same result otherwise,
by means of the pure colour which is involved, and the
proportion of grey by which it is rendered impure. In such a
scale the fundamental elements would be the precise tints of
red, yellow, and blue which are found or assumed to be
primary; the numerical exponents of each colour would depend
upon the arbitrary number of degrees which we interpose
between each two primary colours; and between each pure
colour and absolute blackness. No such numerical scale has,
however, as yet, obtained general acceptation[28\4].
[Note 28\4: The reference to _Fraunhofer's Lines_, as a
means of determining the place of a colour in the prismatic
series, has been objected to, because, as is asserted, the
colours which are in the neighbourhood of each line vary
with the position of the sun, state of the atmosphere and
the like. It is very evident that coloured light refracted
by the prism will not give the same spectrum as white light.
The spectrum given by white light is of course the one here
meant. It is an usual practice of optical experimenters to
refer to the colours of such a spectrum, defining them by
Fraunhofer's Lines.
I do not know whether it needs explanation that the 'first
spectrum' in Newton's rings is a ring of the prismatic
colours.
I have not had an opportunity of consulting Lambert's
_Photometria, sive de mensura et gradibus luminis, colorum,
et umbræ_, published in 1760, nor Mayer's _Commentatio de
Affinitate Colorum_, (1758), in which, I believe, he
describes a chromatometer. The present work is not intended
to be complete as a history; and I hope I have given
sufficient historical detail to answer its philosophical
purpose.]
{346} SECT. IV.--_Scales of Light._
9. _Photometer._--ANOTHER instrument much needed in optical
researches is a _Photometer_, a measure of the intensity of
light. In this case, also, the organ of sense, the eye, is
the ultimate judge; nor has any effect of light, as light,
yet been discovered which we can substitute for such a
judgment. All instruments, such as that of Leslie, which
employ the heating effect of light, or at least all that
have hitherto been proposed, are inadmissible as
photometers. But though the eye can judge of two surfaces
illuminated by light of the same colour, and can determine
when they are equally bright, or which is the brighter, the
eye can by no means decide at sight the proportion of
illumination. How much in such judgments we are affected by
contrast, is easily seen when we consider how different is
the apparent brightness of the moon at mid-day and at
midnight, though the light which we receive from her is, in
fact, the same at both periods. In order to apply a scale in
this case, we must take advantage of the known numerical
relations of light. We are certain that if all other
illumination be excluded, two equal luminaries, under the
same circumstances, will produce an illumination twice as
great as one does; and we can easily prove, from
mathematical considerations, that if light be not enfeebled
by the medium through which it passes, the illumination on a
given surface will diminish as the square of the distance of
the luminary increases. If, therefore, we can by taking a
fraction thus known of the illuminating effect of one
luminary, make it equal to the total effect of another, of
which equality the eye is a competent judge, we compare the
effects of the two luminaries. In order to make this
comparison we may, with Rumford, look at the shadows of the
same object made by the two lights, {347} or with Ritchie,
we may view the brightness produced on two contiguous
surfaces, framing an apparatus so that the equality may be
brought about by proper adjustment; and thus a measure will
become practicable. Or we may employ other methods as was
done by Wollaston[29\4], who reduced the light of the sun by
observing it as reflected from a bright globule, and thus
found the light of the sun to be 10,000,000,000 times that
of Sirius, the brightest fixed star. All these methods are
inaccurate, even as methods of comparison; and do not offer
any fixed or convenient numerical standard; but none better
have yet been devised[30\4].
[Note 29\4: _Phil. Trans._ 1820, p. 19.]
[Note 30\4: Improved Photometers have been devised by
Professor Wheatstone, Professor Potter, and Professor
Steinheil; but they depend upon principles similar to those
mentioned in the text.]
10. _Cyanometer._--As we thus measure the brightness of a
colourless light, we may measure the intensity of any
particular colour in the same way; that is, by applying a
standard exhibiting the gradations of the colour in question
till we find a shade which is seen to agree with the
proposed object. Such an instrument we have in the
_Cyanometer_, which was invented by Saussure for the purpose
of measuring the intensity of the blue colour of the sky. We
may introduce into such an instrument a numerical scale, but
the numbers in such a scale will be altogether arbitrary.
SECT. V.--_Scales of Heat._
11. _Thermometers._--WHEN we proceed to the sensation of
heat, and seek a measure of that quality, we find, at first
sight, new difficulties. Our sensations of this kind are
more fluctuating than those of vision; for we know that the
same object may feel warm to one hand and cold to another at
the same instant, if the hands have been previously cooled
and warmed respectively. Nor can we obtain here, as in the
case of light, self-evident numerical relations of the heat
communicated in given circumstances; for we know that the
{348} effect so produced will depend on the warmth of the
body to be heated, as well as on that of the source of heat;
the summer sun, which warms our bodies, will not augment the
heat of a red-hot iron. The cause of the difference of these
cases is, that bodies do not receive the whole of their
heat, as they receive the whole of their light, from the
immediate influence of obvious external agents. There is no
readily-discovered absolute cold, corresponding to the
absolute darkness which we can easily produce or imagine.
Hence we should be greatly at a loss to devise a
_Thermometer_, if we did not find an indirect effect of heat
sufficiently constant and measurable to answer this purpose.
We discover, however, such an effect in the _expansion_ of
bodies by the effect of heat.
12. Many obvious phenomena show that air, under given
circumstances, expands by the effect of heat; the same is
seen to be true of liquids, as of water, and spirit of wine;
and the property is found to belong also to the metallic
fluid, quicksilver. A more careful examination showed that
the increase of bulk in some of these bodies by increase of
Heat was a fact of a nature sufficiently constant and
regular to afford a means of measuring that previously
intangible quality; and the Thermometer was invented. There
were, however, many difficulties to overcome, and many
points to settle, before this instrument was fit for the
purposes of science.
An explanation of the way in which this was done necessarily
includes an important chapter of the history of Thermotics.
We must now, therefore, briefly notice historically the
progress of the Thermometer. The leading steps of this
progress, after the first invention of the instrument,
were--The establishment of _fixed points_ in the
thermometric scale--The _comparison of the scales_ of
different substances--And the reconcilement of these
differences by some method of interpreting them as
indications of the absolute _quantity of heat_.
13. It would occupy too much space to give in detail the
history of the successive attempts by which {349} these
steps were effected. A thermometer is described by Bacon
under the title _Vitrum Calendare_; this was an air
thermometer. Newton used a thermometer of linseed oil, and
he perceived that the first step requisite to give value to
such an instrument was to fix its scale; accordingly he
proposed his _Scala Graduum Caloris_[31\4]. But when
thermometers of different liquids were compared, it
appeared, from their discrepancies, that this fixation of
the scale of heat was more difficult than had been supposed.
It was, however, effected. Newton had taken freezing water,
or rather thawing snow, as the zero of his scale, which is
really a fixed point; Halley and Amontons discovered (in
1693 and 1702) that the heat of boiling water is another
fixed point; and Daniel Gabriel Fahrenheit, of Dantzig, by
carefully applying these two standard points, produced,
about 1714, thermometers, which were constantly consistent
with each other. This result was much admired at the time,
and was, in fact, the solution of the problem just stated,
the _fixation of the scale of heat_.
[Note 31\4: _Phil. Trans._ 1701.]
14. But the scale thus obtained is a conventional not a
natural scale. It depends upon the fluid employed for the
thermometer. The progress of expansion from the heat of
freezing to that of boiling water is different for mercury,
oil, water, spirit of wine, air. A degree of heat which is
half-way between these two standard points according to a
mercurial thermometer, will be below the half-way point in a
spirit thermometer, and above it in an air thermometer. Each
liquid has its own _march_ in the course of its expansion.
Deluc and others compared the marches of various liquids,
and thus made what we may call a _concordance_ of
thermometers of various kinds.
15. Here the question further occurs: Is there not some
_natural measure_ of the degrees of heat? It appears certain
that there must be such a measure, and that by means of it
all the scales of different liquids must be reconciled. Yet
this does not seem to have occurred at once to men's minds.
Deluc, in speaking {350} of the researches which we have
just mentioned, says[32\4], 'When I undertook these
experiments, it never once came into my thoughts that they
could conduct me with any probability to a table of real
degrees of heat. But hope grows with success, and desire
with hope.' Accordingly he pursued this inquiry for a long
course of years.
[Note 32\4: _Modif. de l'Atmosph._ 1782, p. 303.]
What are the principles by which we are to be guided to the
true measure of heat? Here, as in all the sciences of this
class, we have the general principle, that the secondary
quality, Heat, must be supposed to be perceived in some way
by a material Medium or Fluid. If we take that which is,
perhaps, the simplest form of this hypothesis, that the heat
depends upon the _quantity_ of this fluid, or _Caloric_,
which is present, we shall find that we are led to
propositions which may serve as a foundation for a natural
measure of heat. The _Method of Mixtures_ is one example of
such a result. If we mix together two pints of water, one
hot and one cold, is it not manifest that the temperature of
the mixture must be midway between the two? Each of the two
portions brings with it its own heat. The whole heat, or
caloric, of the mixture is the sum of the two; and the heat
of each half must be the half of this sum, and therefore its
temperature must be intermediate between the temperatures of
the equal portions which were mixed. Deluc made experiments
founded upon this principle, and was led by them to conclude
that 'the dilatations of mercury follow an accelerated march
for successive equal augmentations of heat.'
But there are various circumstances which prevent this
method of mixtures from being so satisfactory as at first
sight it seems to promise to be. The different capacities
for heat of different substances, and even of the same
substance at different temperatures, introduce much
difficulty into the experiments; and this path of inquiry
has not yet led to a satisfactory result. {351}
16. Another mode of inquiring into the natural measure of
heat is to seek it by researches on the _law of cooling_ of
hot bodies. If we assume that the process of cooling of hot
bodies consists in a certain material heat flying off, we
may, by means of certain probable hypotheses, determine
mathematically the law according to which the temperature
decreases as time goes on; and we may assume _that_ to be
the true measure of temperature which gives to the
experimental law of cooling the most simple and probable
form.
It appears evident from the most obvious conceptions which
we can form of the manner in which a body parts with its
superabundant heat, that the hotter a body is, the faster it
cools; though it is not clear without experiment, by what
law the rate of cooling will depend upon the heat of the
body. Newton took for granted the most simple and seemingly
natural law of this dependence: he supposed the rate of
cooling to be _proportional_ to the temperature, and from
this supposition he could deduce the temperature of a hot
iron, calculating from the original temperature and the time
during which it had been cooling. By calculation founded on
such a basis, he graduated his thermometer.
17. But a little further consideration showed that the rate
of cooling of a hot body depended upon the temperature of
the surrounding bodies, as well as upon its own temperature.
Prevost's _Theory of Exchanges_[33\4] was propounded with a
view of explaining this dependence, and was generally
accepted. According to this theory, all bodies radiate heat
to one another, and are thus constantly giving and receiving
heat; and a body which is hotter than surrounding bodies,
cools itself, and warms the surrounding, bodies, by an
exchange of heat for heat, in which they are the gainers.
Hence if _θ_ be the temperature of the bodies, or of the
space, by which the hot body is surrounded, and _θ_ + _t_ the
temperature of the hot body, the rate of cooling will depend
{352} upon the excess of the radiation for a temperature _θ_ +
_t_, above the radiation for a temperature _θ_.
[Note 33\4: _Recherches sur la Chaleur_, 1791. _Hist. Ind.
Sc._ b. x. c. i. sect. 2.]
Accordingly, in the admirable researches of MM. Dulong and
Petit upon the cooling of bodies, it was assumed that the
rate of cooling of the hot body was represented by the
excess of F(_θ_ + _t_) above F(_θ_); where F represented some
mathematical _function_, that is, some expression obtained
by arithmetical operations from the temperatures _θ_ + _t_ and
_θ_; although what these operations are to be, was left
undecided, and was in fact determined by the experiments.
And the result of their investigations was, that the
function is of this kind: when the temperature increases by
equal intervals, the function increases in a continued
geometric proportion[34\4]. This was, in fact, the same law
which had been assumed by Newton and others, with this
difference, that _they_ had neglected the term which depends
upon the temperature of the surrounding space.
[Note 34\4: The formula for the rate of cooling is _ma^(θ +
t) - ma^θ_, where the quantity _m_ depends upon the nature
of the body, the state of its surface, and other
circumstances.--_Ann. Chim._ vii. 150.]
18. This law falls in so well with the best conceptions we
can form of the mechanism of cooling upon the supposition of
a radiant fluid caloric, that it gives great probability to
the scale of temperature on which the simplicity of the
result depends. Now the temperatures in the formulæ just
referred to were expressed by means of the _air
thermometer_. Hence MM. Dulong and Petit justly state, that
while all different substances employed as thermometers give
different laws of thermotical phenomena, their own success
in obtaining simple and general laws by means of the air
thermometer, is a strong recommendation of that as the
_natural scale of heat_. They add[35\4], 'The well-known
uniformity of the principal physical properties of all
gases, and especially the perfect identity of their laws of
dilatation by heat, [a very important discovery of {353}
Dalton and Gay Lussac[36\4],] make it very probable that in
this class of bodies the disturbing causes have not the same
influence as in solids and liquids; and consequently that
the changes of bulk produced by the action of heat are here
in a more immediate dependence on the force which produces them.'
[Note 35\4: _Annales de Chimie_, vii. 153.]
[Note 36\4: _Hist. Ind. Sc._ b. x. c. ii. sect. 1.]
19. Still we cannot consider this point as settled till we
obtain a more complete theoretical insight into the nature
of heat itself. If it be true that heat consists in the
vibrations of a fluid, then, although, as Ampère has
shown[37\4], the laws of radiation will, on mathematical
grounds, be the same as they are on the hypothesis of
emission, we cannot consider the natural scale of heat as
determined, till we have discovered some means of measuring
the caloriferous vibrations as we measure luminiferous
vibrations. We shall only know what the quantity of heat is
when we know what heat itself is;--when we have obtained a
theory which satisfactorily explains the manner in which the
substance or medium of heat produces its effects. When we
see how radiation and conduction, dilatation and
liquefaction, are all produced by mechanical changes of the
same fluid, we shall then see what the nature of that change
is which dilatation really measures, and what relation it
bears to any more proper standard of heat.
[Note 37\4: _Ib._ c. iv.]
We may add, that while our thermotical theory is still so
imperfect as it is, all attempts to divine the true nature
of the relation between light and heat are premature, and
must be in the highest degree insecure and visionary.
Speculations in which, from the general assumption of a
caloriferous and luminiferous medium, and from a few facts
arbitrarily selected and loosely analysed, a general theory
of light and heat is asserted, are entirely foreign to the
course of inductive science, and cannot lead to any stable
and substantial truth.
20. _Other Instruments for measuring Heat._--It does not
belong to our present purpose to speak of {354} instruments
of which the object is to measure, not sensible qualities,
but some effect or modification of the cause by which such
qualities are produced: such, for instance, are the
_Calorimeter_, employed by Lavoisier and Laplace, in order
to compare the _Specific Heat_ of different substances; and
the _Actinometer_, invented by Sir John Herschel, in order
to determine the _effect of the Sun's Rays_ by means of the
heat which they communicate in a given time; which effect
is, as may readily be supposed, very different under
different circumstances of atmosphere and position. The laws
of such effects may be valuable contributions to our
knowledge of heat, but the interpretation of them must
depend on a previous knowledge of the relations which
temperature bears to heat, according to the views just
explained.
SECT. VI.--_Scales of other Qualities._
21. BEFORE quitting the subject of the measures of sensible
qualities, we may observe that there are several other such
qualities for which it would be necessary to have scales and
means of measuring, in order to make any approach to science
on such subjects. This is true, for instance, of Tastes and
Smells. Indeed some attempts have been made towards a
classification of the Tastes of sapid substances, but these
have not yet assumed any satisfactory or systematic
character; and I am not aware that any instrument has been
suggested for _measuring_ either the Flavour or the Odour of
bodies which possess such qualities.
22. _Quality of Sounds._--The same is true of that kind of
difference in sounds which is peculiarly termed their
_Quality_; that character by which, for instance, the sound
of a flute differs from that of a hautbois, when the note is
the same; or a woman's voice from a boy's.
23. _Articulate Sounds._--There is also in sounds another
difference, of which the nature is still obscure, but in
reducing which to rule, and consequently to measure, some
progress has nevertheless been made. {355} I speak of the
differences of sound considered as _articulate_.
Classifications of the sounds of the usual alphabets have
been frequently proposed; for instance, that which arranges
the _Consonants_ in the following groups,:
Sharp. Flat. Sharp Aspirate. Flat Aspirate. Nasal.
p b ph (_f_) bh (_v_) m
k g (hard) kh gh ng
t d th (sharp) th (flat) n
s z sh zh
It is easily perceived that the relations of the sounds in
each of these horizontal lines are analogous; and
accordingly the rules of derivation and modification of
words in several languages proceed upon such analogies. In
the same manner the _Vowels_ may be arranged in an order
depending on their sound. But to make such arrangements
fixed and indisputable, we ought to know the mechanism by
which such modifications are caused. Instruments have been
invented by which some of these sounds can be imitated; and
if such instruments could be made to produce the above
series of articulate sounds, by connected and regular
processes, we should find, in the process, a _measure_ of
the sound produced. This has been in a great degree effected
for the Vowels by Professor Willis's artificial mode of
imitating them. For he finds that if a musical reed be made
to sound through a cylindrical pipe, we obtain by gradually
lengthening the cylindrical pipe, the series of vowels I, E,
A, O, U, with intermediate sounds[38\4]. In this instrument,
then, the length of the pipe would determine the vowel, and
might be used numerically to express it. Such an instrument
so employed would be a measure of vowel quality, and might
be called a _Phthongometer_.
[Note 38\4: _Camb. Trans._ vol. iii. p. 239.]
Our business at present, however, is not with instruments
which might be devised for measuring sensible qualities, but
with those which have been so used, and have thus been the
basis of the sciences in which {356} such qualities are
treated of; and this we have now done sufficiently for our
present purpose.
24. There is another Idea which, though hitherto very
vaguely entertained, has had considerable influence in the
formation, both of the sciences spoken of in the present
Book, and on others which will hereafter come under our
notice: namely, the Idea of Polarity. This Idea will be the
subject of the ensuing Book. And although this Idea forms a
part of the basis of various other extensive portions of
science, as Optics and Chemistry, it occupies so peculiarly
conspicuous a place in speculations belonging to what I have
termed the Mechanico-Chemical Sciences, (Magnetism and
Electricity,) that I shall designate the discussion of the
Idea of Polarity as the Philosophy of those Sciences.
{{357}}
BOOK V.
THE
PHILOSOPHY
OF THE
MECHANICO-CHEMICAL SCIENCES.
En donnant à ces côtés le nom de _poles_, j'appelerai
_polarisation_ la modification qui donne à la lumière des
propriétés relatives à ces poles. J'ai tardé jusqu'à présent
à admettre ce terme dans la description des phénomènes
physiques dont il est question; je n'ai pas osé l'introduire
dans les mémoires où j'ai publié mes dernières expériences;
mais les variétés qu'offre ce nouveau phénomène, et la
difficulté de les décrire, me forcent à admettre cette
nouvelle expression, qui signifie simplement la modification
que la lumière a subie en acquérant de nouvelles propriétés
qui ne sont pas relatives à la direction du rayon, mais
seulement à ses côtés considérés à angles droits et dans un
plan perpendiculaire à sa direction.
Malus (1811), _Mém. de Inst._ tom. xi. p. 106.
{{359}}
BOOK V.
THE PHILOSOPHY OF THE MECHANICO-CHEMICAL SCIENCES.
CHAPTER I.
ATTEMPTS AT THE SCIENTIFIC APPLICATION OF THE IDEA OF
POLARITY.
1. IN some of the mechanical sciences, as Magnetism and
Optics, the phenomena are found to depend upon position (the
position of the magnet, or of the ray of light,) in a
peculiar alternate manner. This dependence, as it was first
apprehended, was represented by means of certain conceptions
of space and force, as for instance by considering the two
_Poles_ of a magnet. But in all such modes of representing
these alternations by the conceptions borrowed from other
ideas, a closer examination detected something superfluous
and something defective; and in proportion as the view which
philosophers took of this relation was gradually purified
from these incongruous elements, and was rendered more
general and abstract by the discovery of analogous
properties in new cases, it was perceived that the relation
could not be adequately apprehended without considering it
as involving a peculiar and independent Idea, which we may
designate by the term _Polarity_.
We shall trace some of the forms in which this Idea has
manifested itself in the history of science. In doing so we
shall not begin, as in other Books of this work we have
done, by speaking of the notion as it is {360} employed in
common use: for the relation of Polarity is of so abstract
and technical a nature, that it is not employed, at least in
any distinct and obvious manner, on any ordinary or
practical occasions. The idea belongs peculiarly to the
region of speculation: in persons of common habits of
thought it is probably almost or quite undeveloped; and even
most of those whose minds have been long occupied by
science, find a difficulty in apprehending it in its full
generality and abstraction, and stript of all irrelevant
hypothesis.
2. _Magnetism._--The name and the notion of _Poles_ were
first adopted in the case of a magnet. If we have two
magnets, their extremities attract and repel each other
alternatively. If the first end of the one attract the first
end of the other, it repels the second end, and conversely.
In order to express this rule conveniently, the two ends of
each magnet are called the _north pole_ and the _south pole_
respectively, the denominations being borrowed from the
poles of the earth and heavens. 'These poles,' as Gilbert
says[1\5], 'regulate the motions of the celestial spheres
and of the earth. In like manner the magnet has its poles, a
northern and a southern one; certain and determined points
constituted by nature in the stone, the primary terms of its
motions and effects, the limits and governors of many
actions and virtues.'
[Note 1\5: _De Magn._ lib. i. c. iii.]
The nature of the opposition of properties of which we speak
may be stated thus:
The North pole of one magnet attracts the South pole of another
magnet.
The North pole of one magnet _repels_ the North pole of another
magnet.
The South pole of one magnet repels the South pole of another
magnet.
The South pole of one magnet _attracts_ the North pole of
another magnet.
It will be observed that the contrariety of position which
is indicated by putting the South pole for the North pole in
either magnet, is accompanied by the {361} opposition of
mechanical effect which is expressed by changing attraction
into repulsion and repulsion into attraction: and thus we
have the general feature of Polarity,--A contrast of
properties corresponding to a contrast of positions.
3. _Electricity._--When the phenomena of Electricity came to
be studied, it appeared that they involved relations in some
respects Analogous to those of magnetism.
Two kinds of electricity were distinguished, the positive
and the negative; and it appeared that two bodies electrized
positively, or two electrized negatively, repelled each
other, like two north or two south magnetic poles; while a
positively and a negatively electrized body attracted each
other, like the north and south poles of two magnets. In
conductors of an oblong form, the electricity could easily
be made to distribute itself so that one end should be
positively and one end negatively electrized; and then such
conductors acted on each other exactly as magnets would do.
But in conductors, however electrized, there is no peculiar
point which can permanently be considered as the _pole_. The
distribution of electricity in the conductor depends upon
external circumstances: and thus, although the phenomena
offer the general character of _polarity_--alternative
results corresponding to alternative positions,--they cannot
be referred to poles. Some other mode of representing the
forces must be adopted than that which makes them emanate
from permanent points as in a magnet.
The phenomena of attraction and repulsion in electrized
bodies were conveniently represented by means of the
hypothesis of _two_ electric _fluids_, a positive and a
negative one, which were supposed to be distributed in the
bodies. Of these fluids, it was supposed that each repelled
its own parts and attracted those of the opposite fluid: and
it was found that this hypothesis explained all the obvious
laws of electric action. Here then we have the phenomena of
polarization explained by a new kind of machinery:--two
opposite fluids {362} distributed in bodies, and supplying
them, so to speak, with their polar forces. This hypothesis
not only explains electrical attraction, but also the
electrical spark: namely, thus: when two bodies, of which
the neighbouring surfaces are charged with the two opposite
fluids, approach near to each other, the mutual attraction
of the fluids becomes more and more intense, till at last
the excess of fluid on the one body breaks through the air
and rushes to the other body, in a form accompanied by light
and noise. When this transfer has taken place, the
attraction ceases, the positive and the negative fluid
having neutralized each other. Their effort was to unite;
and this union being effected, there is no longer any force
in action. Bodies in their natural unexcited condition may
be considered as occupied by a combination of the two
fluids: and hence we see how the production of either kind
of electricity is necessarily accompanied with the
production of an equivalent amount of the opposite kind.
4. _Voltaic Electricity._--Such is the case in Franklinic
electricity,--that which is excited by the common electrical
machine. In studying Voltaic electricity, we are led to the
conviction that the fluid which is in a condition of
momentary _equilibrium_ in electrized conductors, exists in
the state of a _Current_ in the voltaic circuit. And here we
find polar relations of a new kind existing among the
forces. Two voltaic Currents _attract_ each other when they
are moving in the _same_, and _repel_ each other when they
are moving in _opposite_, directions.
But we find, in addition to these, other polar relations of
a more abstruse kind, and which the supposition of two
fluids does not so readily explain. For instance, if such
fluids existed, distinct from each other, it might be
expected that it would be possible to exhibit one of them
separate from the other. Yet in all the phenomena of
electromotive currents, we attempt in vain to obtain one
kind of electricity separately. 'I have not,' says Mr.
Faraday[2\5], 'been able to find a {363} single fact which
could be adduced to prove the theory of two electricities
rather than one, in electric currents; or, admitting the
hypothesis of two electricities, have I been able to
perceive the slightest grounds that one electricity can be
more powerful than the other, or that it can be present
without the other, or that it can be varied or in the
slightest degree affected without a corresponding variation
in the other.' 'Thus,' he adds, 'the polar character of the
powers is rigorous and complete.' Thus, we too may remark,
all the superfluous and precarious parts gradually drop off
from the hypothesis which we devise in order to represent
polar phenomena; and the abstract notion of Polarity--of
equal and opposite powers called into existence by a common
condition--remains unincumbered with extraneous machinery.
[Note 2\5: _Researches_, 516.]
5. _Light._--Another very important example of the
application of the Idea of Polarity is that supplied by the
discovery of the polarization of light. A ray of light may,
by various processes, be modified, so that it has different
properties according to its different _sides_, although this
difference is not perceptible by any common effects. If, for
instance, a ray thus modified, pass perpendicularly through
a circular glass, and fall upon the eye, we may turn the
glass round and round in its frame, and we shall make no
difference in the brightness of the spot which we see. But
if, instead of a glass, we look through a longitudinal slice
of tourmaline, the spot is alternately dark and bright as we
turn the crystal through successive quadrants. Here we have
a contrast of Properties (dark and bright) corresponding to
a contrast of positions, (the position of a line east and
west being contrasted with the position north and south,)
which, as we have said, is the general character of
Polarity. It was with a view of expressing this character
that the term _Polarization_ was originally introduced.
Malus was forced by his discoveries into the use of this
expression. 'We find,' he says, in 1811, 'that light
acquires properties which are relative only to the sides of
the ray,--which are the same for the north and south sides
of the ray, (using {364} the points of the compass for
description's sake only,) and which are different when we go
from the north and south to the east or to the west sides of
the ray. I shall give the name of _poles_ to these sides of
the ray, and shall call _polarization_ the modification
which gives to light these properties relative to these
poles. I have _put off_ hitherto the admission of this term
into the description of the physical phenomena with which we
have to do: I did not _dare_ to introduce it into the
Memoirs in which I published my last observations: but the
variety of forms in which this new phenomenon appears, and
the difficulty of describing them, compel me to admit this
new expression; which signifies simply the modification
which light has undergone in acquiring new properties which
are not relative to the direction of the ray, but only to
its sides considered at right angles to each other, and in a
plane perpendicular to its direction.'
The theory which represents light as an emission of
particles was in vogue at the time when Malus published his
discoveries; and some of his followers in optical research
conceived that the phenomena which he thus described
rendered it necessary to ascribe poles and an axis to each
particle of light. On this hypothesis, light would be
polarized when the axes of all the particles were in the
same direction: and, making such a supposition, it may
easily be conceived capable of transmission through a
crystal whose axis is parallel to that of the luminous
particles, and intransmissible when the axis of the crystal
is in a position transverse to that of the particles.
The hypothesis of particles possessing _poles_ is a rude and
arbitrary assumption, in this as in other cases; but it
serves to convey the general notion of polarity, which is
the essential feature of the phenomena. The term
'polarization of light has sometimes been complained of in
modern times as hypothetical and obscure. But the real cause
of obscurity was, that the Idea of Polarity was, till
lately, very imperfectly developed in men's minds. As we
have seen, the general notion of Polarity,--opposite
properties in opposite {365} directions,--exactly describes
the character of the optical phenomena to which the term is
applied.
It is to be recollected that in optics we never speak of the
_poles_, but of the _plane of polarization_ of a ray. The
word _sides_, which Newton and Malus have used, neither of
them appears to have been satisfied with; Newton, in
employing it, had recourse to the strange Gallicism of
speaking of the _coast_ of usual and of unusual refraction
of a crystal.
The modern theory of optics represents the plane of
polarization of light as depending, not on the position in
which the axes of the luminiferous particles lie, but on the
_direction_ of those _transverse vibrations_ in which light
consists. This theory is, as we have stated in the History,
recommended by an extraordinary series of successes in
accounting for the phenomena. And this hypothesis of
transverse vibrations shows us another mechanical mode,
(besides the hypothesis of particles with axes,) by which we
may represent the polarity of a ray. But we may remark that
the general notion of Polarity, as applied to light in such
cases, would subsist, even if the undulatory theory were
rejected. The idea is, as we have before said, independent
of all hypothetical machinery.
I need not here refer to the various ways in which light may
be polarized; as, for instance, by being reflected from the
surface of water, or of glass, at certain angles, by being
transmitted, through crystals, and in other ways. In all
cases the modification produced, the polarization, is
identically the same property. Nor need I mention the
various kinds of phenomena which appear as contrasts in the
result; for these are not merely light and dark, or white
and black, but red and green, and generally, a colour and
its _complementary_ colour, exhibited in many complex and
varied configurations. These multiplied modes in which
polarized light presents itself add nothing to the original
conception of Polarization: and I shall therefore pass on to
another subject.
6. _Crystallization._--Bodies which are perfectly
crystallized exhibit the most complete regularity and {366}
symmetry of form; and this regularity not only appears in
their outward shape, but pervades their whole texture, and
manifests itself in their cleavage, their transparency, and
in the uniform and determinate optical properties which
exist in every part, even in the smallest fragment of the
mass. If we conceive crystals as composed of particles, we
must suppose these particles to be arranged in the most
regular manner; for example, if we suppose each particle to
have an axis, we must suppose all these axes to be parallel;
for the direction of the axis of the particles is indicated
by the physical and optical properties of the crystal, and
therefore this direction must be the same for every portion
of the crystal. This parallelism of the axes of the
particles may be conceived to result from the circumstance
of each particle having poles, the opposite poles attracting
each other. In virtue of forces acting as this hypothesis
assumes, a collection of small _magnetic_ particles would
arrange themselves in parallel positions; and such a
collection of magnetic particles offers a sort of image of a
crystal. Thus we are led to conceive the particles of
crystals as polarized, and as determined in their
crystalline positions by polar forces. This mode of
apprehending the constitution of crystals has been adopted
by some of our most eminent philosophers. Thus Berzelius
says[3\5], 'It is demonstrated, that the regular forms of
bodies presuppose an effort of their atoms to touch each
other by preference in certain points; that is, they are
founded upon a Polarity;'--he adds, 'a polarity which can be
no other than an electric or magnetic polarity.' In this
latter clause we have the identity of different kinds of
polarity asserted; a principle which we shall speak of in
the next chapter. But we may remark, that even without
dwelling upon this connexion, any notion which we can form
of the structure of Crystals necessarily involves the idea
of Polarity. Whether this polarity necessarily requires us
to believe crystals to be composed of Atoms which exert an
effort to touch {367} each other in certain points by
preference, is another question. And, in agreement with what
has been said respecting other kinds of polarity, we shall
probably find, on a more profound examination of the
subject, that while the Idea of Polarity is essential, the
machinery by which it is thus expressed is precarious and
superfluous.
[Note 3\5: _Essay on the Theory of Chemical Properties_,
1820, p. 113.]
7. _Chemical Affinity._--We shall have, in the next Book, to
speak of Chemical Affinity at some length; but since the
ultimate views to which philosophers have been led, induce
them to consider the forces of Affinity as Polar Forces, we
must enumerate these among the examples of Polarity. In
chemical processes, opposites tend to unite, and to
neutralize each other by their union. Thus an _acid_ or an
_alkali_ combine with vehemence, and form a compound, a
neutral salt, which is neither acid nor alkaline.
This conception of contrariety and mutual neutralization,
involves the Idea of Polarity. In the conception as
entertained by the earlier chemists, the Idea enters very
obscurely: but in the attempts which have more recently been
made to connect this relation (of acid and base), with other
relations, the chemical elements have been conceived as
composed of particles which possess poles; _like_ poles
repelling, and _unlike_ attracting each other, as they do in
magnetic and electric phenomena. This is, however, a rude
and arbitrary way of expressing Polarity, and, as may be
easily shown, involves many difficulties which do not belong
to the Idea itself. Mr. Faraday, who has been led by his
researches to a conviction of the polar nature of the forces
of chemical affinity, has expressed their character in a
more general manner, and without any of the machinery of
particles indued with poles. According to his view, chemical
synthesis and analysis must always be conceived as taking
place in virtue of equal and opposite forces, by which the
particles are united or separated. These forces, by the very
circumstance of their being polar, may be transferred from
point to point. For if we conceive a string of particles,
and if the positive force of the first particle {368} be
liberated and brought into action, its negative force also
must be set free: this negative force neutralizes the
positive force of the next particle, and therefore the
negative force of this particle (before employed in
neutralizing its positive force) is set free: this is in the
same way transferred to the next particle, and so on. And
thus we have a positive force active at one extremity of a
line of particles, corresponding to a negative force at the
other extremity, all the intermediate particles reciprocally
neutralizing each other's action. This conception of the
transfer of chemical action was indeed at an earlier period
introduced by Grotthus[4\5], and confirmed by Davy. But in
Mr. Faraday's hands we see it divested of all that is
superfluous, and spoken of, not as a line of particles, but
as 'an axis of power, having [at every point] contrary
forces, exactly equal, in opposite directions.'
[Note 4\5: DUMAS, _Leçons sur la Philosophie Chimique_, p. 401.]
8. _General Remarks._--Thus, as we see, the notion of
Polarity is applicable to many large classes of phenomena.
Yet the Idea in a distinct and general form is only of late
growth among philosophers. It has gradually been abstracted
and refined from many extraneous hypotheses which were at
first supposed to be essential to it. We have noticed some
of these hypotheses;--as the poles of a _body_; the poles of
the _particles_ of a fluid; _two_ opposite fluids; a single
fluid in _excess_ and _defect_; transverse _vibrations_. To
these others might be added. Thus Dr. Prout[5\5] assumes
that the polarity of molecules results from their _rotation_
on their axes, the opposite motions of contiguous molecules
being the cause of opposite (positive and negative)
polarities.
[Note 5\5: _Bridgewater Treatise_, p. 559.]
But none of these hypotheses can be proved by the fact of
Polarity alone; and they have been in succession rejected
when they had been assumed on that ground. Thus Davy, in
1826, speaking of chemical forces says[6\5], 'In assuming
the idea of two ethereal, subtile, elastic {369} fluids,
attractive of the particles of each other, and repulsive as
to their own particles, capable of combining in different
proportions with bodies, and according to their proportions
giving them their specific qualities and rendering them
equivalent masses, it would be natural to refer the action
of the poles to the repulsions of the substances combined
with the excess of one fluid, and the attractions of those
united to the excess of the other fluid; and a history of
the phenomena, not unsatisfactory to the reason, might in
this way be made out. But as it is possible likewise to take
an entirely different view of the subject, on the idea of
the dependence of the results upon the primary attractive
powers of the parts of the combination on a single subtile
fluid, I shall not enter into any discussion on this obscure
part of the theory.' Which of these theories will best
represent the case, will depend upon the consideration of
other facts, in combination with the polar phenomena, as we
see in the history of optical theory. In like manner Mr.
Faraday proved by experiment[7\5] the errour of all theories
which ascribe electro-chemical decomposition to the
attraction of the poles of the voltaic battery.
[Note 6\5: _Phil. Tr._ 1826, p. 415.]
[Note 7\5: _Researches_, p. 495, &c.]
In order that they may distinctly image to themselves the
Idea of Polarity, men clothe it in some of the forms of
machinery above spoken of; yet every new attempt shows them
the unnecessary difficulties in which they thus involve
themselves. But on the other hand it is difficult to
apprehend this Idea divested of all machinery; and to
entertain it in such a form that it shall apply at the same
time to magnetism and electricity, galvanism and chemistry,
crystalline structure and light. The Idea of _Polarity_
becomes most pure and genuine, when we entirely reject the
conception of _Poles_, as Faraday has taught us to do in
considering electro-chemical decomposition; but it is only
by degrees and by effort that we can reach this point of
abstraction and generality. {370}
9. There is one other remark which we may here make. It was
a maxim commonly received in the ancient schools of
philosophy, that 'Like attracts Like:' but as we have seen,
the universal maxim of Polar Phenomena is, that Like
_repels_ Like, and attracts Unlike. The north pole attracts
the south pole, the positive fluid attracts the negative
fluid; opposite elements rush together; opposite motions
reduce each other to rest. The permanent and stable course
of things is that which results from the balance and
neutralization of contrary tendencies. Nature is constantly
labouring after repose by the effect of such tendencies; and
so far as Polar Forces enter into her economy, she seeks
harmony by means of discord, and unity by opposition.
Although the Idea of Polarity is as yet somewhat vague and
obscure, even in the minds of the cultivators of physical
science, it has nevertheless given birth to some general
principles which have been accepted as evident, and have had
great influence on the progress of science. These we shall
now consider.
{{371}}
CHAPTER II.
OF THE CONNEXION OF POLARITIES.
1. IT has appeared in the preceding chapter that in cases in
which the phenomena suggest to us the idea of Polarity, we
are also led to assume some material machinery as the mode
in which the polar forces are exerted. We assume, for
instance, globular particles which possess poles, or the
vibrations of a fluid, or two fluids attracting each other;
in every case, in short, some hypothesis by which the
existence and operation of the Polarity is embodied in
geometrical and mechanical properties of a medium; nor is it
possible for us to avoid proceeding upon the conviction that
some such hypothesis must be true; although the nature of
the connexion between the mechanism and the phenomena must
still be indefinite and arbitrary.
But since each class of Polar Phenomena is thus referred to
an ulterior cause, of which we know no more than that it has
a polar character, it follows that _different_ Polarities
may result from the _same_ cause manifesting its polar
character under different aspects. Taking, for example, the
hypothesis of globular particles, if electricity result from
an action dependent upon the _poles_ of each globule,
magnetism may depend upon an action in the _equator_ of each
globule; or taking the supposition of transverse vibrations,
if polarized light result directly from such _vibrations_,
crystallization may have reference to the _axes_ of the
elasticity of the _medium_ by which the vibrations are
rendered transverse,--so far as the polar character only of
the phenomena is to be accounted for. I say this _may_ be
so, _in so far_ only as the polar character of the phenomena
is concerned; for whether the relation of {372} electricity
to magnetism, or of crystalline forces to light, can really
be explained by such hypotheses, remains to be determined by
the facts themselves. But since the first necessary feature
of the hypothesis is, that it shall give polarity, and since
an hypothesis which does this, may, by its mathematical
relations, give polarities of different kinds and in
different directions, any two co-existent kinds of polarity
may result from the same cause, manifesting itself in
various manners.
The conclusion to which we are led by these general
considerations is, that two co-existing classes of polar
phenomena _may_ be effects of the same cause. But those who
have studied such phenomena more deeply and attentively
have, in most or in all cases, arrived at the conviction
that the various kinds of Polarity in such cases _must_ be
connected and fundamentally identical. As this conviction
has exercised a great influence, both upon the discoveries
of new facts and upon the theoretical speculations of modern
philosophers, and has been put forward by some writers as a
universal principle of science, I will consider some of the
cases in which it has been thus applied.
2. _Connexion of Magnetic and Electric Polarity._--The polar
phenomena of electricity and magnetism are clearly analogous
in their laws: and obvious facts showed at an early period
that there was some connexion between the two agencies.
Attempts were made to establish an evident and definite
relation between the two kinds of force, which attempts
proceeded upon the principle now under
consideration;--namely, that in such cases, the two kinds of
Polarity must be connected. Professor Œrsted, of Copenhagen,
was one of those who made many trials founded upon this
conviction: yet all these were long unsuccessful. At length,
in 1820, he discovered that a galvanic current, passing at
right angles near to a magnetic needle, exercises upon it a
powerful deflecting force. The connexion once detected
between magnetism and galvanism was soon recognized as
constant and universal. It was represented in different
hypothetical modes by different persons; some considering
the galvanic {373} current as the primitive axis, and the
magnet as constituted of galvanic currents passing round it
at right angles to the magnetic axis; while others conceived
the magnetic axis as the primitive one, and the electric
current as implying a magnetic current round the wire. So
far as many of the general relations of these two kinds of
force were concerned, either mode of representation served
to express them; and thus the assumption that the two
Polarities, the magnetic and the electric, were
fundamentally identical, was verified, so far as the
phenomena of magnetic attraction, and the like, were
concerned.
I need not here mention how this was further confirmed by
the experiments in which, by means of the forces thus
brought into view, a galvanic wire was made to revolve round
a magnet, and a magnet round a galvanic wire;--in which
artificial magnets were constructed of coils of galvanic
wire;--and finally, in which the galvanic spark was obtained
from the magnet. The identity which sagacious speculators
had divined even before it was discovered, and which they
had seen to be universal as soon as it was brought to light,
was completely manifested in every imaginable form.
The relation of the electric and magnetic Polarities was
found to be, that they were _transverse_ to each other, and
this relation exhibited under various conditions of form and
position of the apparatus, gave rise to very curious and
unexpected perplexities. The degree of complication which
this relation may occasion, may be judged of from the number
of constructions and modes of conception offered by Œrsted,
Wollaston, Faraday, and others, for the purpose of framing a
technical memory of the results. The magnetic polarity gives
us the north and south poles of the needle; the electric
polarity makes the current positive and negative; and these
pairs of opposites are connected by relations of situation,
as above and below, right and left; and give rise to the
resulting motion of the needle one way or the other. {374}
3. Ampère, by framing his hypotheses of the action of
voltaic currents and the constitution of magnets, reduced
all these technical rules to rigorous deductions from one
general principle. And thus the vague and obscure persuasion
that there _must_ be _some_ connexion between Electricity
and Magnetism, so long an idle and barren conjecture, was
unfolded into a complete theory, according to which magnetic
and electromotive actions are only two different
manifestations of the same forces; and all the
above-mentioned complex relations of polarities are reduced
to one single polarity, that of the electro-dynamic current.
4. As the Idea of Polarity was thus firmly established and
clearly developed, it became an instrument of reasoning.
Thus it led Ampère to maintain that the original or
elementary forces in electro-dynamic action could not be as
M. Biot thought they were, a statical _couple_, but must be
directly opposite to each other. The same idea enabled Mr.
Faraday to carry on with confidence such reasonings as the
following[8\5]: 'No other known power has like direction
with that exerted between an electric current and a magnetic
pole; it is tangential, while all other forces acting at a
distance are direct. Hence if a magnetic pole on one side of
a revolving plate follow its course by reason of its
obedience to the tangential force exerted upon it by the
very current of electricity which it has itself caused; a
similar pole on the other side of the plate should
immediately set it free from this force; for the currents
which have to be formed by the two poles are in contrary
directions.' And in Article 1114 of his _Researches_, the
same eminent philosopher infers that if electricity and
magnetism are considered as the results of a peculiar agent
or condition, exerted in determinate directions
perpendicular to each other, one must be by some means
convertible into the other; and this he was afterwards able
to prove to be the case in fact.
[Note 8\5: _Researches_, 244.]
{375} Thus the principle that the Co-existent Polarities of
magnetism and electricity are connected and fundamentally
identical, is not only true, but is far from being either
vague or barren. It has been a fertile source both of
theories which have, at present, a very great probability,
and of the discovery of new and striking facts. We proceed
to consider other similar cases.
5. _Connexion of Electrical and Chemical Polarities._--The
doctrine that the chemical forces by which the elements of
bodies are held together or separated, are identical with
the polar forces of electricity, is a great discovery of
modern times; so great and so recent, indeed, that probably
men of science in general have hardly yet obtained a clear
view and firm hold of this truth. This doctrine is now,
however, entirely established in the minds of the most
profound and philosophical chemists of our time. The
complete development and confirmation of this as of other
great truths, was preceded by more vague and confused
opinions gradually tending to this point; and the progress
of thought and of research was impelled and guided, in this
as in similar cases, by the persuasion that these
co-existent polarities could not fail to be closely
connected with each other. While the ultimate and exact
theory to which previous incomplete and transitory theories
tended is still so new and so unfamiliar, it must needs be a
matter of difficulty and responsibility for a common reader
to describe the steps by which truth has advanced from point
to point. I shall, therefore, in doing this, guide myself
mainly by the historical sketches of the progress of this
great theory, which, fortunately for us, have been given us
by the two philosophers who have played by far the most
important parts in the discovery, Davy and Faraday.
It will be observed that we are concerned here with the
progress of theory, and not of experiment, except so far as
it is confirmatory of theory. In Davy's Memoir[9\5] of 1826,
on the Relations of Electrical and {376} Chemical Changes,
he gives the historical details to which I have alluded.
Already in 1802 he had conjectured that all chemical
decompositions might be polar. In 1806 he attempted to
confirm this conjecture, and succeeded, to his own
satisfaction, in establishing[10\5] that the combinations
and decompositions by electricity were referable to the law
of electrical attractions and repulsions; and advanced the
hypothesis (as he calls it), that chemical and electrical
attractions were produced by the same cause, acting in one
case on particles, in the other on masses. This hypothesis
was most strikingly confirmed by the author's being able to
use electrical agency as a more powerful means of chemical
decomposition than any which had yet been applied.
'Believing,' he adds, 'that our philosophical systems are
exceedingly imperfect, I never attached much importance to
this hypothesis; but having formed it after a copious
induction of facts, and having gained by the application of
it a number of practical results, and considering myself as
much the author of it as I was of the decomposition of the
alkalies, and having developed it in an elementary work as
far as the present state of chemistry seemed to allow, I
have never,' he says, 'criticised or examined the manner in
which different authors have adopted or explained it,
contented, if in the hands of others, it assisted the
arrangements of chemistry or mineralogy, or became an
instrument of discovery.' When the doctrine had found an
extensive acceptance among chemists, attempts were made to
show that it had been asserted by earlier writers: and
though Davy justly denies all value to these pretended
anticipations, they serve to show, however dimly, the
working of that conviction of the Connexion of Co-existent
Properties which all along presided in men's minds during
this course of investigation. 'Ritter and Winterl have been
quoted,' Davy says[11\5], 'among other persons, as having
imagined or anticipated the relation between electrical
powers and chemical affinities before the discovery of the
pile {377} of Volta. But whoever will read with attention
Ritter's "Evidence that Galvanic action exists in organised
nature," and **Winterl's _Prolusiones ad Chemiam sæculi decimi
noni_, will find nothing to justify this opinion.' He then
refers to the Queries of Newton at the end of his Optics.
'These,' he says, 'contain more grand and speculative views
that might be brought to bear upon this question than any
found in the works of modern electricians; but it is very
unjust to the experimentalists who by the laborious
application of new instruments, have discovered novel facts
and analogies, to refer them to any such suppositions as
that all attractions, chemical, electrical, magnetical, and
gravitative, may depend upon the same cause.' It is
perfectly true, that such vague opinions, though arising
from that tendency to generalize which is the essence of
science, are of no value except so far as they are both
rendered intelligible, and confirmed by experimental
research.
[Note 9\5: _Phil. Trans._ 1826, p. 383.]
[Note 10\5: _Phil. Trans._ 1826, p. 389.]
[Note 11\5: _Ibid._ p. 384.]
The phenomena of chemical decomposition by means of the
voltaic pile, however, led other persons to views very
similar to those of Davy. Thus Grotthus in 1805[12\5]
published an hypothesis of the same kind. 'The pile of
Volta,' he says, 'is an electrical magnet, of which each
element, that is, each pair of plates, has a positive and a
negative pole. The consideration of this polarity suggested
to me the idea that a similar polarity may come into play
between the elementary particles of water when acted upon by
the same electrical agent; and I avow that this thought was
for me a flash of light.'
[Note 12\5: _Ann. Chim._ lxviii. 54.]
6. The thought, however, though thus brought into being, was
very far from being as yet freed from vagueness,
superfluities, and errours. I have elsewhere noticed[13\5]
Faraday's remark on Davy's celebrated Memoir of 1806; that
'the mode of action by which the effects take place is
stated very generally, so generally, indeed, that probably a
dozen precise schemes of electro-chemical action might be
drawn up, differing {378} essentially from each other, yet
all agreeing with the statement there given.' When Davy and
others proceeded to give a little more definiteness and
precision to the statement of their views, they soon
introduced into the theory features which it was afterwards
found necessary to abandon. Thus[14\5] both Davy, Grotthus,
Riffault, and Chompré, ascribed electrical decomposition to
the action of the _poles_, and some of them even pretended
to assign the proportion in which the force of the pole
diminishes as the distance from it increases. Faraday, as I
have already stated, showed that the polarity must be
considered as residing not only in what had till then been
called the _poles_, but at every point of the circuit. He
ascribed[15\5] electro-chemical decomposition to internal
forces, residing in the _particles_ of the matter under
decomposition, not to external forces, exerted by the poles.
Hence he shortly afterwards[16\5] proposed to reject the
word _poles_ altogether, and to employ instead, the term
_electrode_, meaning the doors or passages (of whatever
surface formed) by which the decomposed elements pass out.
What have been called the _positive_ and _negative_ poles he
further termed the _Anode_ and _Cathode_; and he introduced
some other changes in nomenclature connected with these. He
then, as I have related in the History[17\5], invented the
Volta-electrometer, which enabled him to measure the
quantity of voltaic action, and this he found to be
identical with the quantity of chemical affinity; and he was
thus led to the clearest view of the truth towards which he
and his predecessors had so long been travelling, that
electrical and chemical forces are identical[18\5].
[Note 13\5: _Hist. Ind. Sc._ b. xiv. c. ix. sect. 1.]
[Note 14\5: See Faraday's Historical Sketch, _Researches_,
481-492.]
[Note 15\5: Art. 524.]
[Note 16\5: In 1834. Eleventh Series of Researches. Art. 662.]
[Note 17\5: _Hist. Ind. Sc._ b. xiv. c. ix. sect. 2.]
[Note 18\5: Arts. 915, 916, 917.]
7. It will, perhaps, be said that this beautiful train of
discovery was entirely due to experiment, and not to any _à
priori_ conviction that co-existent polarities {379} must be
connected. I trust I have sufficiently stated that such an
_à priori_ principle could not be proved, nor even
understood, without a most laborious and enlightened use of
experiment; but yet I think that the doctrine, when once
fully unfolded, exhibited clearly, and established as true,
takes possession of the mind with a more entire conviction
of its certainty and universality, in virtue of the
principle we are now considering. When the theory has
assumed so simple a form, it appears to derive immense
probability (to say the least) from its simplicity. Like the
laws of motion, when stated in its most general form, it
appears to carry with it its own evidence. And thus this
great theory borrows something of its character from the
Ideas which it involves, as well as from the Experiments by
which it was established.
8. We may find in many of Mr. Faraday's subsequent
reasonings, clear evidence that this idea of the Connexion
of Polarities, as now developed, is not limited in its
application to facts already known experimentally, but, like
other ideas, determines the philosopher's researches into
the unknown, and gives us the _form_ of knowledge even
before we possess the _matter_. Thus, he says, in his
Thirteenth Series[19\5], 'I have long sought, and still
seek, for an effect or condition which shall be to statical
electricity what magnetic force is to current electricity;
for as the lines of discharge are associated with a certain
transverse effect, so it appeared to me impossible but that
the lines of tension or of inductive action, which of
necessity precede the discharge, should also have their
correspondent transverse condition or effect.' Other similar
passages might be found.
[Note 19\5: Art. 1658.]
I will now consider another case to which we may apply the
Principle of Connected Polarities.
9. _Connexion of Chemical and Crystalline Polarities._--The
close connexion between the Chemical Affinity and the
Crystalline Attraction of elements cannot be overlooked.
Bodies never crystallize but when their elements combine
chemically; and solid bodies which {380} combine, when they
do it most completely and exactly, also crystallize. The
forces which _hold together_ the elements of a crystal of
alum are the same forces which make it a _crystal_. There is
no distinguishing between the two sets of forces.
Both _chemical_ and _crystalline_ forces are _polar_, as we
stated in the last chapter; but the polarity in the two
cases is of a different kind. The polarity of chemical
forces is then put in the most distinct form, when it is
identified with electrical polarity; the polarity of the
particles of crystals has reference to their geometrical
form. And it is clear that these two kinds of polarity must
be connected. Accordingly, Berzelius expressly asserts[20\5]
the necessary identity of these two polarities. 'The regular
forms of bodies suppose a polarity which _can be_ no other
than an electric or magnetic polarity.' This being so
seemingly inevitable, we might expect to find the electric
forces manifesting some relation to the definite directions
of crystalline forms. Mr. Faraday tried, but in vain, to
detect some such relation. He attempted to ascertain[21\5]
whether a cube of rock crystal transmitted the electrical
force of tension with different intensity along and across
the axis of the crystal. In the first specimen there seemed
to be some difference; but in other experiments, made both
with rock crystal and with calc spar, this difference
disappeared. Although therefore we may venture to assert
that there must be some very close connexion between
electrical and crystalline forces, we are, as yet, quite
ignorant what the nature of the connexion is, and in what
kind of phenomena it will manifest itself.
[Note 20\5: _Essay on Chemical Prop._ 113.]
[Note 21\5: _Researches_. Art. 1689.]
10. _Connexion of Crystalline and Optical
Polarities._--Crystals present to us _optical_ phenomena
which have a manifestly polar character. The double
refraction, both of uniaxal and of biaxal crystals, is
always accompanied with opposite polarization of the two
rays; and in this and in other ways light is polarized in
directions dependent upon the axes of the crystalline form,
that is, on the directions of the polarities of the {381}
crystalline particles. The identity of these two kinds of
polarity (crystalline and optical) is too obvious to need
insisting on; and it is not necessary for us here to decide
by what hypothesis this identity may most properly be
represented. We may hereafter perhaps find ourselves
justified in considering the crystalline forces as
determining the _elasticity_ of the luminiferous ether to be
different in _different directions_ within the crystal, and
thus as determining the refraction and polarization of the
light which the crystal transmits. But at present we merely
note this case as an additional example of the manifest
connexion and fundamental identity of two co-existent
polarities.
11. _Connexion of Polarities in general._--Thus we find that
the Connexion of different kinds of Polarities, magnetic,
electric, chemical, crystalline, and optical, is certain as
a truth of experimental science. We have attempted to show
further that in the minds of several of the most eminent
discoverers and philosophers, such a conviction is something
more than a mere empirical result: it is a principle which
has regulated their researches while it was still but
obscurely seen and imperfectly unfolded, and has given to
their theories a character of generality and self-evidence
which experience alone cannot bestow.
It will, perhaps, be said that these doctrines,--that
scientific researches may usefully be directed by principles
in themselves vague and obscure;--that theories may have an
evidence superior to and anterior to experience;--are
doctrines in the highest degree dangerous, and utterly at
variance with the soundest maxims of modern times respecting
the cultivation of science.
In the justice and wisdom of this caution I entirely agree:
and although I have shown that this principle of the
_Connexion of Polarities_, rightly interpreted and
established in each case by experiment, involves profound
and comprehensive truths; I think it no less important to
remark that, at least in the present stage of our knowledge,
we can make no use of this principle without taking care, at
every step, to determine by {382} clear and decisive
experiments, its proper meaning and application. All
endeavours to proceed otherwise have led, and must lead, to
ignorance and confusion. Attempts to deduce from our bare
Idea of Polarity, and our fundamental convictions respecting
the connexion of polarities, theories concerning the forces
which really exist in nature, can hardly have any other
result than to bewilder men's minds, and to misdirect their
efforts.
So far, indeed, as this persuasion of a connexion among
apparently different kinds of agencies, impels men, engaged
in the pursuit of knowledge, to collect observations, to
multiply, repeat, and vary experiments, and to contemplate
the result of these in all aspects and relations, it may be
an occasion of the most important discoveries. Accordingly
we find that the great laws of phenomena which govern the
motions of the planets about the sun, were first discovered
by Kepler, in consequence of his scrutinizing the recorded
observations with an intense conviction of the existence of
geometrical and arithmetical harmonies in the solar system.
Perhaps we may consider the discovery of the connexion of
magnetism and electricity by Professor Œrsted in 1820, as an
example somewhat of the same kind; for he also was a
believer in certain comprehensive but undefined relations
among the properties of bodies; and in consequence of such
views entertained great admiration for the _Prologue to the
Chemistry of the Nineteenth Century_, of Winterl, already
mentioned. M. Œrsted, in 1803, published a summary of this
work; and in so doing, praised the views of Winterl as far
more profound and comprehensive than those of Lavoisier.
Soon afterwards a Review of this publication appeared in
France[22\5], in which it was spoken of as a work only fit
for the dark ages, and as the indication of a sect which had
for some time 'ravaged Germany,' and inundated that country
with extravagant and unintelligible mysticism. It was,
therefore, a kind of triumph to M. Œrsted to be, after {383}
some years' labour, the author of one of the most remarkable
and fertile physical discoveries of his time.
[Note 22\5: _Ann. Chim._, Tom. 1. (1804), p. 191.]
12. It was not indeed without some reason that certain of
the German philosophers were accused of dealing in doctrines
vast and profound in their aspect, but, in reality,
indefinite, ambiguous, and inapplicable. And the most
prominent of such doctrines had reference to the principle
now under our consideration; they represented the properties
of bodies as consisting in certain polarities, and professed
to deduce, from the very nature of things, with little or no
reference to experiment, the existence and connexion of
these polarities. Thus Schelling, in his _Ideas towards a
Philosophy of Nature_, published in 1803, says[23\5],
'Magnetism is the universal act of investing Multiplicity
with Unity; but the universal form of the reduction of
Multiplicity to Unity is the Line, pure Longitudinal
Extension: hence Magnetism is determination of pure
Longitudinal Extension; and as this manifests itself by
absolute Cohesion, Magnetism is the determination of
absolute Cohesion.' And as Magnetism was, by such reasoning,
conceived to be proved as a universal property of matter,
Schelling asserted it to be a confirmation of his views when
it was discovered that other bodies besides iron are
magnetic. In like manner he used such expressions as the
following[24\5]: 'The threefold character of the Universal,
the Particular, and the Indifference of the two,--as
expressed in their Identity, is Magnetism, as expressed in
their Difference, is Electricity, and as expressed in the
Totality, is Chemical Process. Thus these forms are only one
form; and the Chemical Process is a mere transfer of the
three Points of Magnetism into the Triangle of Chemistry.'
[Note 23\5: P. 223.]
[Note 24\5: P. 486.]
It was very natural that the chemists should refuse to
acknowledge, in this fanciful and vague language,
(delivered, however, it is to be recollected, in 1803,) an
anticipation of Davy's doctrine of the identity of
electrical and chemical forces, or of Œrsted's {384}
electro-magnetic agency. Yet it was perhaps no less natural
that the author of such assertions should look upon every
great step in the electro-chemical theory as an illustration
of his own doctrines. Accordingly we find Schelling
welcoming, with a due sense of their importance, the
discoveries of Faraday. When he heard of the experiment in
which electricity was produced from common magnetism, he
fastened with enthusiasm upon the discovery, even before he
knew any of its details, and proclaimed it at a public
meeting of a scientific body[25\5] as one of the most
important advances of modern science. We have (he thus
reasoned) three effects of polar forces;--Electro-chemical
Decomposition, Electrical Action, Magnetism. Volta and Davy
had confirmed experimentally the identity of the two former
agencies: Œrsted showed that a closed voltaic circuit
acquired magnetic properties: but in order to exhibit the
identity of electric and magnetic action it was requisite
that electric forces should be extricated from magnetic.
This great step Faraday, he remarked, had made, in producing
the electric spark by means of magnets.
[Note 25\5: Ueber Faraday's _Neueste Entdeckung_. München. 1832.]
13. Although conjectures and assertions of the kind thus put
forth by Schelling involve a persuasion of the pervading
influence and connexion of polarities, which persuasion has
already been confirmed in many instances, they involve this
principle in a manner so vague and ambiguous that it can
rarely, in such a form, be of any use or value. Such views
of polarity can never teach us in what cases we are and in
what we are not expected to find polar relations; and indeed
tend rather to diffuse error and confusion, than to promote
knowledge. Accordingly we cannot be surprized to find such
doctrines put forward by their authors as an evidence of the
small value and small necessity of experimental science.
This is done by the celebrated metaphysician Hegel, in his
_Encyclopædia_[26\5]. 'Since,' {385} says he, 'the plane of
incidence and of reflection in simple reflection is the same
plane, when a second reflector is introduced which further
distributes the illumination reflected from the first, the
position of the first plane with respect to the second
plane, containing the direction of the first reflection and
of the second, has its influence upon the position,
illumination or darkening of the object as it appears by the
second reflection. This influence must be the strongest when
the two planes are what we must call _negatively_ related to
each other:--that is, when they are at right angles.' 'But,'
he adds, 'when men infer (as Malus has done) from the
modification which is produced by this situation, in the
illumination of the reflection, that the molecules of light
in themselves, that is, on their different sides, possess
different physical energies; and when on this foundation,
along with the phenomena of entoptical colours therewith
connected, a wide labyrinth of the most complex theory is
erected; we have then one of the most remarkable examples of
the _inferences_ of physics from experiment.' If Hegel's
reasoning prove anything, it must prove that polarization
always accompanies reflection under such circumstances as he
describes: yet all physical philosophers know that in the
case of metals, in which the reflection is most complete,
light is not completely polarized at any angle; and that in
other substances the polarization depends upon various
circumstances which show how idle and inapplicable is the
account which he thus gives of the property. His
self-complacent remark about the inferences of physics from
experiment, is intended to recommend by comparison his own
method of considering the nature of 'things in themselves;'
a mode of obtaining physical truth which had been more than
exhausted by Aristotle, and out of which no new attempts
have extracted anything of value since his time.
[Note 26\5: Sec. 278.]
14. Thus the general conclusion to which we are led on this
subject, is, that the persuasion of the existence and
Connexion or Identity of various Polarities in nature,
although very naturally admitted, and in many {386} cases
interpreted and confirmed by observed facts, is of itself,
so far as we at present possess it, a very insecure guide to
scientific doctrines. When it is allowed to dictate our
theories, instead of animating and extending our
experimental researches, it leads only to errour, confusion,
obscurity, and mysticism.